The Cauchy‐Riemann operator on smooth Fréchet‐valued functions with exponential growth on rotated strips | Zendy

Kruse Karsten | Zendy

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The Cauchy‐Riemann operator on smooth Fréchet‐valued functions with exponential growth on rotated strips

Author(s) -

Kruse Karsten

Publication year - 2019

Publication title -

pamm

Language(s) - English

Resource type - Journals

ISSN - 1617-7061

DOI - 10.1002/pamm.201900141

Subject(s) - cauchy–riemann equations , mathematics , cauchy distribution , operator (biology) , strips , exponential growth , mathematical analysis , exponential function , initial value problem , pure mathematics , riemann hypothesis , algorithm , biochemistry , chemistry , repressor , transcription factor , gene

We study the Cauchy‐Riemann operator ∂ ¯ on spaces ℰ γ ( Ω ( θ ) , E ) of smooth functions on an open set Ω ( θ ) ⊂ ℝ 2 with values in a complex Fréchet space E which grow exponentially (γ = 1) on strips rotated by an angle θ. We state sufficient conditions for the surjectivity of ∂ ¯ : ℰ γ ( Ω ( θ ) , E ) → ℰ γ ( Ω ( θ ) , E ) .

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